On the propagation of regularity for solutions of the Zakharov-Kuznetsov equation

In this paper, we focus on the Zakharov-Kuznetsov (ZK) equation in the n-dimensional setting with n >= 2 and investigate its smoothness properties. We extend the well-known regularity propagation phenomenon observed in the 2D and 3D cases, where the regularity of the initial data on certain half-spaces propagates with infinite speed, to the case where the regularity of the initial data is measured on a fractional scale. To achieve this, we introduce new localization formulas that enable us to describe the regularity of the solution on a specific class of subsets in Euclidean space. This work provides insights into the regularity behavior of solutions of the ZK equation in higher dimensions and with more general initial data.